Go to Modify Panel and click the Pick Object button and select the Source mesh in the viewport.

Apply a material with a bitmap texture to the Target object. Enable Show Map in Viewport.

Select Target object. In the Modify Panel apply an UVW Frame modifier to it. Click the pick button ( named None ) and pick the UVW Frame object in the viewport.
By now, the Source object's UVW mesh is linked to the Target object's mesh by the UVW Frame. This is an active link. If you move the Target mesh, or the UVW Frame, the UVW Mesh in the Source object will be affected in real time.

Convert Source object to an Editable Mesh, select it's bottom faces and Detach them as a new element. Rotate the new element so all faces are facing up, and move them to the side. Increase the size of the UVW Frame as needed.

Apply a Relax modifier to the Source mesh. Increase the iterations to remove all UVW stretching from the Source object.